Question

Stock X has a 10.0% expected return, a beta coefficient of 0.9, and a 40% standard deviation of expected returns. Stock Y has a 12.5% expected return, a beta coefficient of 1.2, and a 20.0% standard deviation. The risk-free rate is 6%, and the market risk premium is 5%. The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the questions below.

Open spreadsheet

1. Calculate each stock's coefficient of variation. Round your answers to two decimal places. Do not round intermediate calculations.

   CV_x =

   CV_y =

2. Which stock is riskier for a diversified investor?

   1. For diversified investors the relevant risk is measured by standard deviation of expected returns. Therefore, the stock with the lower standard deviation of expected returns is more risky. Stock Y has the lower standard deviation so it is more risky than Stock X.
   2. For diversified investors the relevant risk is measured by beta. Therefore, the stock with the higher beta is less risky. Stock Y has the higher beta so it is less risky than Stock X.
   3. For diversified investors the relevant risk is measured by beta. Therefore, the stock with the higher beta is more risky. Stock Y has the higher beta so it is more risky than Stock X.
   4. For diversified investors the relevant risk is measured by standard deviation of expected returns. Therefore, the stock with the higher standard deviation of expected returns is more risky. Stock X has the higher standard deviation so it is more risky than Stock Y.
   5. For diversified investors the relevant risk is measured by beta. Therefore, the stock with the lower beta is more risky. Stock X has the lower beta so it is more risky than Stock Y.
   
   _____IIIIIIIVV

3. Calculate each stock's required rate of return. Round your answers to two decimal places.

   r_x = %

   r_y = %

4. On the basis of the two stocks' expected and required returns, which stock would be more attractive to a diversified investor?

   _________Stock XStock Y

5. Calculate the required return of a portfolio that has $7,000 invested in Stock X and $4,000 invested in Stock Y. Do not round intermediate calculations. Round your answer to two decimal places.

   r_p = %

6. If the market risk premium increased to 6%, which of the two stocks would have the larger increase in its required return?

   _________Stock XStock Y

Answer 1

a) Coefficient of Variation is given by

CV = standard Deviation/Expected return

So, CV (X) = 40%/10% = 4.00

& CV (Y) = 20%/12.5% = 1.60

b) For a diversified investor, Beta provides the relevant measure of risk because standard deviation provides for the total risk i.e systematic and unsystematic (diversifiable) risk. A well diversified investor only cares about the systematic risk. The higher the Beta, the higher the risk and hence the correct option is Option III

c) Required rate of return can be calculated from CAPM model

R_x = risk free rate +Beta_x * Market risk premium

So, R_x = 6% +0.9*5%

= 10.50%

&   R_Y = 6% +1.2* 5%

=12.00%

d) The Alpha of a stock is the difference between Expected and required returns

So , Alpha (X) = Expected return of X- Required return of X

= 10% -10.50%

= -0.50%

&  Alpha (Y) = Expected return of Y- Required return of Y

= 12.50%- 12%

=0.50%

As the Alpha of Stock Y is bigger,it is more attractive to a diversified investor